$-6tu - tv - t - 3 = -10u - 1$ Solve for $t$.
Solution: Combine constant terms on the right. $-6tu - tv - t - {3} = -10u - {1}$ $-6tu - tv - t = -10u + {2}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $-6{t}u - 1{t}v - 1{t} = -10u + 2$ Factor out the $t$ ${t} \cdot \left( -6u - v - 1 \right) = -10u + 2$ Isolate the $t$ $t \cdot \left( -{6u - v - 1} \right) = -10u + 2$ $t = \dfrac{ -10u + 2 }{ -{6u - v - 1} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{10u - 2}{6u + v + 1}$